This paper addresses an open question of how to devise numerical schemes for approximate deconvolution fluid flow models that are efficient, unconditionally stable, and optimally accurate. We propose, analyze and test a scheme for these models that has each of these properties for the case of homogeneous Dirichlet velocity boundary conditions. There are several important components to the deriv...

We propose a novel second order in time, decoupled and unconditionally stable numerical scheme for solving the Cahn-Hilliard-Darcy (CHD) system which models two-phase flow in porous medium or in a Hele-Shaw cell. The scheme is based on the ideas of second order convex-splitting for the Cahn-Hilliard equation and pressure-correction for the Darcy equation. We show that the scheme is uniquely sol...

Saul’yev-type asymmetric schemes have been widely used in solving diffusion and advection equations. In this work, we show that Saul’yev-type schemes can be derived from the exponential splitting of the semidiscretized equation which fundamentally explains their unconditional stability. Furthermore, we show that optimal schemes are obtained by forcing each scheme’s amplification factor to match...

This paper presents a new analysis method on space force telepresence teleoperation system. Since there exists huge time delay in the communication channel between the master and slave sides, it will lead to the system instability and reduce operation ability. The study of this issue is to find out the factors that impact the system unconditional stability. The study method is to use the differ...

In this paper we propose a new method for stable numerical integration of the dynamic Cosserat equations for rods, which constitute a mechanical framework for the physically based modeling of slender structures like DNA strands, drill strings, marine cables or human hair. Our integration method is well-established in the field of structural dynamics and has the major advantage of unconditional ...

We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes equations as a perturbed vector diffusion equation, instead of as a perturbed Stokes system. To illustrate the advantages of this view, we provide a simple pro...

The majority of children placed into foster care are separated from their siblings upon entering the child welfare system. Some research suggests that siblings enjoy more stable home environments and fewer behavioral problems when placed together in care. The sibling relationship may provide stability, consistency, and unconditional positive regard to the children most at risk for poor outcomes...

We present a novel class of high-order space–time finite element schemes for the Poisson–Nernst–Planck (PNP) equations. prove that our are mass conservative, positivity preserving, and unconditionally energy stable any order approximation. To best knowledge, this is first (arbitrarily) accurate PNP equations simultaneously achieve all these three properties. This accomplished via (1) using elem...